Changing to the pronoun 'he' destroys the parallelism. "Mary's rabbit is fat but lively" is parallel.

I had to look up "parallelism". It means repetition of key grammatical elements, but the definition is qualitative, not exact. You do have parallelism in "is fat" vs "is lively", but that just isn't very much. "Is" followed by two different adjectives just isn't very interesting. On the other hand, "Mary's rabbit is fat and happy but her kangaroo is thin and sad" gives us a bit more to chew on.

Thank you so much. You are amazing!